... regard an image as a sample of a stochastic process. Forcontinuous images, the image function F(x, y, t) is assumed to be a member of a con-tinuous three-dimensional stochastic process with space ... represented as a sum of amplitude-weighted Dirac delta functions by the sifting integral, (1.2-6)where is the weighting factor of the impulse located at coordinates inthe x–y plane, as shown ... ωxωy,()=Gxy,()14π2 H ωxωy,()F ωxωy,()i ωxx ωyy+(){}exp ωxd ωyd∞–∞∫∞–∞∫=6CONTINUOUS IMAGE MATHEMATICAL CHARACTERIZATION (1.2-1)In specific cases, the mapping may be many-to-few,...
... the post-retinal transfer functions of Figure 2.5-3. Undoubtedly, both retinal and post-retinal mechanismsare responsible for the chromatic adaption effect. Further analysis and testing arerequired ... An observer is shown two sine-wave grating transpar-encies, a reference grating of constant contrast and spatial frequency and a variable-contrast test grating whose spatial frequency is set ... blood capillaries. Inside the choroid is the retina, which is com-posed of two types of receptors: rods and cones. Nerves connecting to the retinaleave the eyeball through the optic nerve bundle....
... , tristimulus units of the primaries as governed by(3.3-13)Integrating each side of Eq. 3.3-13 over and invoking the sifting integral gives thecone signal for the color (C). Thus(3.3-14)By ... T1, T2, T3 may be regarded as tristimulus values ina retinal cone color coordinate system. The tristimulus values of the retinal conecolor coordinate system are related to the XYZ system ... light. In a subtractive colorsystem, which is the basis of most color photography and color printing, a whitelight sequentially passes through cyan, magenta, and yellow filters to reproduce acolored...
... performed by linearly interpo-lating points along separable orthogonal coordinates of the continuous imagefield. The resultant interpolated surface of Figure 4.3-4b, connecting pixels A, B,C, D, is ... these numbers are then used to reconstruct a con-tinuous image for viewing. Image samples nominally represent some physical mea-surements of a continuous image field, for example, measurements ... ωydωys2⁄–ωys2⁄∫ωxs2⁄–ωxs2⁄∫=114IMAGE SAMPLING AND RECONSTRUCTIONwhere Ai, Bi, Ci, Di are weighting factors. The weighting factors are determined bysatisfying two sets of extraneous conditions:1. at x...
... CHARACTERIZATIONChapter 1 presented a mathematical characterization of continuous image fields.This chapter develops a vector-space algebra formalism for representing discreteimage fields from a deterministic and ... power-spectral density of a discrete image random process may bedefined, in analogy with the continuous power spectrum of Eq. 1.4-13, as the two-dimensional discrete Fourier transform of its ... Gaussian density, are rarely foundin the literature. Huhns (7) has developed a technique of generating high-order den-sities in terms of specified first-order marginal densities and a specified...
... which a nonlinearamplification weighting of the continuous signal to be quantized is performed,followed by linear quantization, followed by an inverse weighting of the quantizedamplitude. Thus, ... reconstruction level within the range to canbe determined by minimization of with respect to . Setting(6.1-6)yields (6.1-7)FIGURE 6.1-2. Quantization decision and reconstruction levels.prj()E ... are two major forms of numeric representation: realand integer. Real numbers are stored in floating-point form, and typically have alarge dynamic range with fine precision. Integer numbers can...
... applications in image processing require a discretization of the superpositionintegral relating the input and output continuous fields of a linear system. For exam-ple, image blurring by an optical system, ... general term is described by(7.2-6)where , with and denoting the upper and lower index limits.If the ultimate objective is to estimate the continuous ideal image field by pro-cessing the physical ... AND CONVOLUTIONwhere is a weighting coefficient for the particular quadrature formulaemployed. Usually, a rectangular quadrature formula is used, and the weightingcoefficients are unity. In...
... based on computational efficiency. In some computing structures, the Hart-ley transform may be more efficiently computed, while in other computing environ-ments, the Fourier transform may be ... cosine transform of a image can be computed by reflecting the imageabout its edges to obtain a array, taking the FFT of the array and thenextracting the real parts of the Fourier transform (15). ... fluctuationvector. This results in(8.4-10)where(8.4-11a)(8.4-11b)are vectors. The process continues until the full transform(8.4-12)is obtained where . It should be noted that the intermediate...
... obtainedby analytically performing the convolution operation of Eq. 9.4-8c and evaluatingthe resulting continuous function at points . In practice, the analytic convo-lution is often difficult ... one-dimensional continuous signal of wide extent which isbandlimited such that its Fourier transform is zero for greater than a cut-off frequency . This signal is to be convolved with a continuous impulse ... Also, it is often possible to render the filter matrix sparse bysetting small-magnitude elements to zero without seriously affecting computationalaccuracy (1).In subsequent sections, the structure...
... retention of fine image detail. Several nonlinear techniques are presented below.Mastin (15) has performed subjective testing of several of these operators.FIGURE 10.3-8. Homomorphic filtering on the ... form by replacingthe discrete probability distributions of Eq. 10.2-2 by continuous probability densi-ties. The resulting approximation is(10.2-4)gdTfc{}= f1fcfC≤≤g1gdgD≤≤PRgdbd={}PRfcac={}PRfcac={}c ... (10.3-2b)Mask 3: (10.3-2c)These arrays, called noise cleaning masks, are normalized to unit weighting so thatthe noise-cleaning process does not introduce an amplitude bias in the processedimage....
... paperplus any spectral losses resulting from filters or optical elements, and kx is an expo-sure constant that is controllable by an aperture or exposure time setting. Equation11.3-1 assumes a ... Figure 11.3-1. In this material, silver halide grains are suspended ina transparent layer of gelatin that is deposited on a glass, acetate, or paper backing.If the backing is transparent, a transparency ... then the negative transparency is illuminated to expose negativereflection print paper. The resulting silver density on the developed paper is thenproportional to the light intensity that exposed...
... constraint(12.6-1)where S is a smoothing matrix, M is an error-weighting matrix, and e denotes aresidual scalar estimation error. The error-weighting matrix is often chosen to beFIGURE 12.5-3. Wiener image ... RESTORATION349extraction operation. Without weighting, errors at the observation boundarycompletely destroy the estimate in the boundary region, but with weighting therestoration is subjectively satisfying, ... increased by setting bR = 2.0. The higher degree of blurgreatly increases the ill-conditioning of the blur matrix, and the residual error information of the modified observation after weighting leads...